I play a plant/energy dom and have no problems soloing.
It can be a little slow because dominators don't have the greatest damage output around but now I've got the flytrap there's a little ravenous bud to help me out!
On the energy side, power boost helps with the confuse duration (seed of confusion is mass confuse you can take at level 8 IIRC, very handy) and hold duration on IMO the not as good as i was expecting Vines.
I would advise getting stamina early too, but that's pretty much a given these days.
As I said, soloing is not a problem and with the plant set you get one of the coolest looking pets in the game!
I find my Dominator is most effective in small teams, preferably with Brutes and Corruptors, and free of Stalkers and MMs.
Solo I find it much harder to control aggro than with my Controller.
I would say Stealth is a must for a soloing dominator.
I really should do something about this signature.
Hmmm I find stalkers a real benefit to my dominator, good stalkers know they can get crits on held foes, so I dont have to worry about anyone I've held already and can move on.
For a solo dom I' recomend Ice or Energy secondry cause of Power Boost.
Possibly Grav as the primary, some attacks in primary as well, a tank like pet, and a foe phase shift for when it all goes wrong.
"Well, they found my diary today.
They were appropriately appalled
at the discovery of the eight victims
They're now putting it all together.
Women wrapped in silk
with one leg missing
Eight legs, one body, silk,
spider, brilliant!"
For soloing I would have said Grav / Energy too (in fact I was thinking the benefits of such a char yesterday).
Grav / Psi might be worthwhile too as it'd provide a wide spread of damage types plus a +regen power in Psi for regening your health, although thats really only effective with larger Mobs.
Plants get a +health regen power in the Spirit Tree which again could be helpful for soloing.
Fire Control is a bit AOE heavy for soloing I feel. The AOE immobilise, disorientate, hotfeet & the AOE hold are all great on teams but a bit End hungry for soloing.
You could also aim to try and get the Medicine Pool. Of course the disadvantage is that you need to take a power that can only be applied to others to get your self heal.
For a solo dominator I'd say fire/eng. Fire simply because of the pets. They are fast, have great damage and theres three of em 
. They die fairly quick tho so a fast reacharge time might be in order if you do not have any kind of support powers (medicine pool). I agree that fire is abit heavy on endurance so get ready to slot with endurance in mind.
I know very little about dominator secondaries but energy seems pretty decent with their power boost and fairly strong melee attacks.
My Mind/Icy Dom isn't very high level, but it has absolutely no problems solo (even against Elite Bosses), and I don't think it will. At L2 you can have the following 3 ranged attacks:
Mesmerise (single target Sleep & Psionic damage, with bonus accuracy so rarely misses)
Dominate (single target Hold & Psionic damage, with bonus accuracy so rarely misses)
Ice Bolt (single target Slow, -recharge & Cold damage)
All 3 have decent duration, fast recharge (easy to stack them on bosses) and a hard-to-resist damage type. Against a typical 3-minion spawn you can put one to sleep, hold another and slow the third. After the third dies you should be able to kill the other two without being attacked by them at all. Also because you're using so many control powers constantly your Domination bar fills up very quickly (can often use it twice per mission - a great way to top up your Endurance so you can keep killing with little downtime). So you've just left the tutorial and you already have a great attack chain for safe soloing.
Icy Assault may not have as much damage as Energy, but it's safer (every attack has Slow and -recharge), should be less resistable than most other damage types, and still gets Power Boost. Mind Control has the best area control in the game including confuse powers so the enemy are too busy killing each other to notice you 
The Mind/Icy combination might not be as fast at killing as say Fire/Energy (although Fire doesn't get Imps til 32), but it's going to be safer solo and probably with much less downtime.
Last week I was actually in a team with two other Doms (both Ice/Ice) - that's the most Doms I've seen in one place since beta 
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Plants get a +health regen power in the Spirit Tree which again could be helpful for soloing.
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You could also aim to try and get the Medicine Pool. Of course the disadvantage is that you need to take a power that can only be applied to others to get your self heal.
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The spirit tree from plant/* isnt that great, long recharge & not a burst heal (stealth and/or medicin pool is more beneficial).
Heal other pays off alot if your set has a pet (& with stealth you can run past the boss to get the pet to tank the first hits if nedeed incase you dont have dom-bar filled).
If your set has a confuse power: six slots. Also your single hold gets 6 slots, nothing less of six.
I'm a firm believer that fire/nrg dominator will be lethal in PvE especially in solo, if you can stick it out till level 32 once you have imps, your all sorted. Energy assualt has highest damage out off all secondaries and fire is most damaging primary aswell as having reasonable control, you should be lethal in PvE, aswell as solo PvP. Try it out, fire imps are incredibly cool!
I'm a firm believer that fire/nrg dominator will be lethal in PvE especially in solo, if you can stick it out till level 32 once you have imps, your all sorted. Energy assualt has highest damage out off all secondaries and fire is most damaging primary aswell as having reasonable control, you should be lethal in PvE, aswell as solo PvP. Try it out, fire imps are incredibly cool!
My fire dominator is good
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Just thought I'd add a quick plug for Ice/Ice - 37 levels so far, and is probably the safest I've ever felt running missions and the like - the -speed, -recharge of Shiver, AA, Chilling Embrace and, well, every single one of your attacks stacks to slow the mobs to a crawl (not even mentioning the confuse pulse on AA), ice slick is just evil (I've never yet seen ANY mob run over it without falling) and at 32, jack just plain trivialises most solo fights - sure, the Imps do more damage, but Jack hits like a runaway train when he's enticed to get up close and personal, he can take more damage than the imps, and he gets a melee hold to help lock down the spawns. The only thing about Ice/ice is that, like all ice powersets, it sucks end like nobody's business - you will pray for stamina at 20....
That and with both ice powersets, taking all 3 of shiver, artic air and chilling embrace is overkill, but hey, it gives you more spaces for all those other powers you wanted to take 
Didn't take shiver, already spending end to slow people enough, and Jack Frost's CE helps too.
Love the melee ability of Ice/Ice, primary and secondry are really suited for it. It's fun, dont get me wrong, but I like having team support, so my end lasts longer. I think Grav/En would be a bit more end friendly is all
"Well, they found my diary today.
They were appropriately appalled
at the discovery of the eight victims
They're now putting it all together.
Women wrapped in silk
with one leg missing
Eight legs, one body, silk,
spider, brilliant!"
I just rolled a Plants/Fire dom and spend a lot of time soloing. How do you think I'll get on?
I just made a Mind/Energy, im not too bothered with solo, but I'd like to know if its possable
OK, it seems that while in a team setting is where I strive, it seems to be harder finding:
a.) A team in general...
b.) A team who won't incur me tons of debt I spend hours clearing.
c.) A team with any knowledge of how MY AT works and what my job is! Honestly, how is a FF Defender expected to match the damage of a Eng/Blaster!
So, I decided to go the path my brother favors well... and that is Solo.
I read a couple guides on Dominators, and read about the diffrent pets they have, and have decided three power sets which are in the running. Fire, Ice, and Plant.
It also gave me some good tips of soloing. I AM seriously considering grabbing Stealth, for the 'ghosting' side of door missions! I LOVED this idea, and kudos to Waybreaker on the US forums for introducing me to this techinque.
I realise that playing a Dom solo is not going to be easy. But I don't play for "easy", I play for the challenge, and this is certainly a challenge I will embrace. I will team at times, but am aiming to mostly solo.
I suppose, I don't have to have the matching assault set for the primary, but if I can, I certainly will...
Any imput for ANY of the three builds will be GREATLY appericated.